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ICSE Class X Notes 2025 : Mathematics

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Bharati Gulajkar
Lokhandwala Foundation School (LFS), Kandivali East, Mumbai
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SECTION A Q1 MCQ) 1) The ratio in which the X - axis divides the line joining the points (- 3 6) and (2, - 8) is: (a) 2 : l (b) 3 : 2 .l'(c) 2: 3 (d) 3 : 4 2) The equation of the line whose inclination is 45 0 and which intersects they - axis at the point (0, -4) is: (a) x- y = 4 (b) x + y = 4 (c) y- X = 4 (d) x- y = - 4 3) If lines 3y = 9x 2 and 5y = kx 2 represent opposite sides of a square, the value of k is (a) 12 (b) 10 (c) 18 (d) 15 4) If x R, the solution set of 6 3(2 4) < 12 a) { : ,0 < 1} b) : ,0 < 1} b) {0,1} c) None of These 5) Mr. R.K. Nair gets Rs. 6455 at the end of one year at the rate of 14% p.a. in a Recurring Deposit Account. Find the monthly instalment. a) Rs. 300 b) Rs. 500 c) Rs. 100 d) Rs. 250 6) For the following transaction within Delhi, find the value of the following: CGST =? SGST=? IGST=? Given that, MRP = Rs.12000, Discount%= 30%, GST= 18% a) Rs 0, Rs 0, Rs 1512 b) Rs 1512, Rs 1512, Rs 0 c) Rs 0, Rs 0, Rs 756 d) Rs 756, Rs 756, Rs 0 7) Mrs Tendon has two sons, one being exactly one year older than the other. At percentage, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the percent ages of her sons. a) 2 years, 5 years b) 5 years, 2 years c) 5 years, 4 years d)4 years, 5 years 8) If both ax3 + 2x3- 3 and x3 - ax + 4 leave the same remainder when divided by x - 2, find a. 1 a) b) 10 9) Let A= [ 3 0 3 3 d) 10 10 3 5 2 ] [ ] B = [ ], Then 10. 5 2 a) x = -3 , y = -7 10) If c) 10 b) x = 10 , y = 4 c) x = 3 , y = -10 d) x = 8 , y = -7 3 +4 + 3 5 = 9 then x is 3 +4 3 5 a) 5 b) 6 c) 7 d) 8 1 3 2 3 Q2) a ) How many terms of the series 20, 19 , 18 , .must be taken so that their sum is 300. b) If a: b: c: d, show that c) ( ) 2 = ( ) 2 + 2 2 + 2 A wholesaler buys a clock from a manufacturer for 4000. He marks the price of the clock 25% above his cost price and sells it to a retailer at a 10% discount on the marked price. If the rate GST is 18%, find [4] i) the marked price. ii) the retailer's cost price inclusive of tax. iii) GST paid by the wholesaler. d) Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axes). (i) (ii) (iii) (iv) (v) Plot A(4, 4), B (4, -6) and C (8, 0), the vertices of a triangle ABC. Reflect ABC on the y-axis and name it as A B C Write the coordinates of the image A , B and C Give a geometrical name for the figure AA'C B BC. Identify -the line of symmetry of AA'C B BC SECTION B Question 1. (a) The midpoint of the line segment joining (2a, 4) and (- 2, 2b) is (1, 2a + 1). Find the value of a and b. [3] (b) Find the value(s) of k for which the following equation has real and equal roots. (k+4) x 2 + (k+1) x +1 = 0 3 + 3 76 c) If 3 3 = 49 use properties of proportion to find out (i) a:b (ii) [3] [4] 2 2 2 2 2 2 Question 2: (a) The fourth term of an A.P is 11 and the eighth term exceeds twice the fourth term by 5. Find the A.P. [3] (b) Mrs. Shetty has a recurring deposit account in a bank of 2000 per month at the rate of 10% p.a. If she gets 83,100 at the time of maturity, find the total time in years, for which the account was held. [3] (c) Equation of line L1 is y = -2. [4] i) Write the slope of line L2 if L2 is the bisector of X OY. ii) Write the coordinates of point M. iii) Find the equation of line L2 Question 3: (a) A grocer bought some baskets of fruit for 1500. Five baskets of fruit were lost in the transit. He sold each of the rest for 10 more than he paid for them and made neither profit nor loss. Find the number of baskets of fruit bought. [3] (b) In PQR, MN is parallel to QR and 3 = 2= , Find : i) MN:QR ii) Area ( OMN) : Area ( ORQ) (c) If a, b, c are in continued proportion, prove that : a2b2c 2 (a-4 + b-4 + c-4 ) = b-2 (a4 + b4 + c4) [3] [4] Question 4: (a) Point P(3,-5) is reflected to point P in the x-axis. Also, point P on reflection in the line x = -1 is mapped as P [3] i) Write the coordinates of P and P . ii) Find the ratio in which the line segment P P is divided by the y-axis. 3 7 0 2 1 5 (b) If A = Let A= [ [3] ] ,B= [ ] and C =[ ] , find AB-5C 2 4 5 3 4 6 (c) ) If the 1st term of an AP is 4 and the sum of first 7 terms is equal to one fourth of the sum of next 7 terms, then (i) show that a20=-110 (ii) Find the sum of 1st 30 terms [4]

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